A Mathematician's Apology is a beautiful read, by definitions both plain and, to some degree, those elaborated in the essay itself.
One interesting thing about the relevancy of the essay is the potential change in the aesthetics of mathematics in wake of the proof of the Four Color Theorem. Personally, I have to believe that some day someone will find a proof that has all the elegance mathematicians are looking for.
"We do not want many ‘variations’ in the proof of a
mathematical theorem: ‘enumeration of cases’, indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way."
If you consider his constant foil in Chess, it's fun to think that perhaps he'd see some degree of beauty in computer algorithms that solve the many enumerations of chess in far more "general" and "surprising" ways.
One interesting thing about the relevancy of the essay is the potential change in the aesthetics of mathematics in wake of the proof of the Four Color Theorem. Personally, I have to believe that some day someone will find a proof that has all the elegance mathematicians are looking for.
"We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases’, indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way."
If you consider his constant foil in Chess, it's fun to think that perhaps he'd see some degree of beauty in computer algorithms that solve the many enumerations of chess in far more "general" and "surprising" ways.